Each of the questions given below consists of three statements, numbered I, II and II respectively. Please read the question and the statements carefully and decide which of the statement(s) is/are necessary to answer the question.

1)

What is the speed of the train ?

I. The train crosses $300$ metres long platform in $21$ seconds.

II. The train crosses another stationary train of equal length in $19\frac{1}{2}$ seconds.

III. The train crosses a signal pole in $9\frac{3}{4}$ seconds.

A) I and II only

B) I and either II or III only

C) II and either I or II only

D) III and either I or II only

E) None of these

Option B

### Explanation:

Let the speed of the train be $x$ m/sec.

Time taken to cross a platform = (Length of train + Length of platform) / Speed of the train

Time taken by the train to cross a stationary train = (Sum of the lengths of the train) / Speed of moving train

Time taken to cross a signal pole = Length of train / Speed of train

I gives, $21=\frac{(l+300)}{x}$; II gives, $\frac{39}{2}$ $=\frac{2l}{x}$; III gives, $\frac{39}{4}$ $=\frac{l}{x}$

Thus, (I and II) or (I and III) give $x$.

$\therefore$ Correct answer is (B).